Precalculus Examples

$4 x^{4} - 4$

Step 1

Factor $4$ out of $4 x^{4} - 4$ .

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Step 1.1

Factor $4$ out of $4 x^{4}$ .

$4 (x^{4}) - 4$

Step 1.2

Factor $4$ out of $- 4$ .

$4 (x^{4}) + 4 (- 1)$

Step 1.3

Factor $4$ out of $4 (x^{4}) + 4 (- 1)$ .

$4 (x^{4} - 1)$

Step 2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$4 ({(x^{2})}^{2} - 1)$

Step 3

Rewrite $1$ as $1^{2}$ .

$4 ({(x^{2})}^{2} - 1^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{2}$ and $b = 1$ .

$4 ((x^{2} + 1) (x^{2} - 1))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Rewrite $1$ as $1^{2}$ .

$4 ((x^{2} + 1) (x^{2} - 1^{2}))$

Step 5.1.2

Factor.

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Step 5.1.2.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$4 ((x^{2} + 1) ((x + 1) (x - 1)))$

Step 5.1.2.2

Remove unnecessary parentheses.

$4 ((x^{2} + 1) (x + 1) (x - 1))$

Step 5.2

Remove unnecessary parentheses.

$4 (x^{2} + 1) (x + 1) (x - 1)$

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